Nonabelian superconductors: vortices and confinement in SQCD

Abstract

We study nonabelian vortices (flux tubes) in SU(N) gauge theories, which are responsible for the confinement of (nonabelian) magnetic monopoles. In particular a detailed analysis is given of N = 2 SQCD with gauge group SU(3) deformed by a small adjoint chiral multiplet mass. Tuning the bare quark masses (which we take to be large) to a common value m, we consider a particular vacuum of this theory in which an SU(2) subgroup of the gauge group remains unbroken. We consider 5 ≥ N f ≥ 4 flavors so that the SU(2) sub-sector remains non asymptotically free: the vortices carrying nonabelian fluxes may be reliably studied in a semi-classical regime. We show that the vortices indeed acquire exact zero modes which generate global rotations of the flux in an SU(2) C+F group. We study an effective world sheet theory of these orientational zero modes which reduces to an N = 2 O(3) sigma model in (1+1) dimensions. Mirror symmetry then teaches us that the dual SU(2) group is not dynamically broken.

SO and USp Kähler and hyper-Kähler quotients and lumps

“…If there exists a divergence in the Kähler potential which cannot be removed by the Kähler transformations, it indicates that the moduli parameters included in the divergent terms are non-normalizable. Let us substitute an expansion of the lump solution with respect to z −1 40) into the Kähler potential (4.33) and expand it as well…”

“…After the discovery of the U(N C ) non-Abelian vortices [39,40], one remarkable new development is an extension to vortices in U(1)×SO(N C ) gauge theories [58] and U(1)×G ′ gauge theories with an arbitrary simple group G ′ [59]. This was done by imposing G ′ invariant constraints on the moduli matrix, and the conditions for the local vortices in these theories have been found.…”

Multi-vortices are wall vortices: A numerical proof

“…This fact is very general and applies also in the multi-monopole case [14]. It will be interesting to see if the bag mechanism works also in more general theories that contain solitons: nonabelian vortices [18], semi-local strings [20], Chern-Simon theories [19] and noncommutative field theories [21].…”

Magnetic impurity inspired Abelian Higgs vortices

“…As a result, it would require infinite energy to break free a bonded pair of a monopole and an anti-monopole placed in a type-II superconductor. This phenomenon, known as the monopole confinement, was proposed by Mandelstam [23,24], Nambu [27], and 't Hooft [40,41], and has served as a profound source of thoughts [33] for the understanding of quark confinement where the underlying Abelian Higgs model platform is extended into various supersymmetric gauge field theory models and the classical Meissner effect is elevated into its supersymmetric versions so that the Nielsen-Olesen magnetic strings become colored ones [3,7,8,10,12,14,15,26,35,36]. See [9,11,21,34,37,38,44,45] for surveys and further literature.…”